题目
The equation of a curve is
Find an equation of the normal to the curve at the point . Give your answer in the form , where , and are integers to be found.
题目中文翻译
一条曲线的方程为
求该曲线在点 处的法线方程。答案写成 的形式,其中 、 和 是待求的整数。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程;仅给出计算器答案而没有过程,不予评分。除非题目另有精度要求,非精确数值答案保留 3 位有效数字,以度为单位的角度保留 1 位小数。
解答
解法一
思路
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对根式用链式法则。代入切点求切线斜率,再取负倒数求法线。
答题过程
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The derivative is
At , the square root is , so . The normal slope is . Its equation is , or